Nucleation Barrier for Volume‐Conserving Shape Changes of Faceted Crystals

Abstract

This paper considers volume-conserving shape changes of small faceted particles or cavities; these changes are driven by surface-energy reduction. If these changes require normal motion of the facets (singular surfaces), and if the perimeter free energy p (per unit area) of a nucleus of a new facet layer is comparable to a typical surface free energy ( Ϸ 1 J/m 2 ), the energy barrier is prohibitively large for facets larger than a limiting size of approximately a nanometer unless they are intersected by dislocations that provide a source of steps. In the absence of such dislocations, particles that contain these facets are immobilized in their initial shapes. If p < , the limiting facet size is increased by a factor of approximately / p .

Equilibrium shape of nickel crystal

“…Another possibility which seems more relevant to the current case is that these F o r P e e r R e v i e w O n l y 16 surfaces are kinetically-stabilized metastable ones and the unexpected extent of occupancy is merely a consequence of a sluggish kinetics for the removal of these surfaces and the formation of new surfaces of a lower energy [13,20]. As was extensively reviewed in Ref.…”

“…Though the unexpected surfaces were observed, the rank of the energies of each surface was always in conformity with that predicted by the model. In this regard, O n l y 14 the abnormality in the rank of the pure nickel currently observed may be attributed to the fact that none of the crystallites could reach its true equilibrium state due to a significant energy barrier for a removal and formation of facet surfaces [13,20]. This is also strongly supported by the fact that the relative surface energies estimated from the carburized nickel crystallites, whose surface energy anisotropy, equivalently step free energy that determines the nucleation energy barrier for the removal and This indicates that the lower energy of {110} surfaces compared with that of {100} surfaces both theoretically expected and experimentally observed in the pure nickel system may be due to a reconstruction effect which is only dominant in the enthalpy-dominant faceted crystals [28].…”

“…However, when a morphological change of a crystal is highly dependent on a surface diffusion due to a limited supply of the atomic flux, the driving force is mostly not enough to remove those energetically unstable surfaces, because even the removal of a faceted surface has an energy barrier [13,20]. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 F o r P e e r R e v i e w O n l y 18 and etc.…”

“…One that is the most straightforward, though it is only qualitatively acceptable [13][14][15] is to monitor the shape of isolated crystals in a closed system at a specific temperature of interest [16,17]. When a consensus on the shape of the majority of crystals is reached, the shape can be approximated as the ECS.…”

“…The other is to analyze a so-called negative shape of crystals from nano-sized annealed cavities [18,19]. From the experimental point of view, the latter method is easier and more reliable since the size of cavities can be as small as a few nanometers, which allows the shape to reach the equilibrium state relatively easier [13,20]. However, a couple of disadvantages of this method is that it only provides two-dimensional information, which is not quite practical in analyzing the ECS with a low symmetry, and the applicability of the technique is usually confined to ceramic systems that are brittle enough to generate crack-induced cavities.…”